/tJU. 


U.S.  DEPARTMENT  OF  AGRICULTURE, 

BUREAU  OF  PLANT  [NDUSTRY— Circular  No.  32. 
■    \i  U  W  \Y,  Chi<  i  of  Bureau. 


MOISTURE  CONTENT  AM)  SHRINKAGE 

IN  GRAIN. 


•I.  W.  T.  DUVEL, 

Assistant  in  Ch  ^rge  op  L  moratory  Meth<  ids. 
Grain  Si  \ \ i> irdization. 


,     09 


WASHINGTON  :  GOVERNMENT  PRINTING  OFFICE  :   1»0» 


\ 


'■  •»*(« 


BUREAU    OF   PLANT    INDUSTRY. 


Chief  of  Bureau,  Beverly  T.  Galloway. 
Assistant  Chief  of  Bureau,  Albert  F.  Woods. 
Editor,!.  E.  Rockwell. 
Chief  Clerk,  James  E.  Jonj  s. 
[Cir.32] 
9 


]i.  P.  I      175. 


MOISTURE  CONTENT  AND  SHRINKAG 

IN  GRAIN. 


INTRODUCTION. 

The  moisture  content  and  the  shrinkage  or  loss  in  the  weight  of 
grain  have  been  the  cause  of  man}  misunderstandings  between  grain 
merchants  and  the  operators  of  elevators  and  commercial  grain  driers 
because  the  shrinkage  and  the  reduction  in  the  percentage  of  moisture, 
resulting  from  the  drying  of  grain,  do  not  correspond.  Moreover, 
«mce  the  development  of  the  practical  and  rapid  method  for  deter- 
mining the  moisture  content  of  grain,  as  described  bj  Brown  and 
Duvi'l  in  a  former  publication  of  this  Bureau,"  these  misunderstand- 
ings have  become  much  more  pronounced.  Investigations  have 
revealed  the  fact  thai  occasionally  operators  of  elevators  and  com- 
mercial grain  driers  have  even  been  accused  of  rendering  insufficient 
returns  on  grain  dried  because  the  loss  in  weight  due  t<>  drying  always 
exceeds  the  percentage  reduction  in  moisture. 

LOSS  OF  MATERIAL  IN  HANDLING. 

In  the  handling  of  grain  through  an  elevator,  commercial  grain 
drier,  or  over  a  cpnveyor,  there  is  always  a  slight  loss  in  weighl  due 
to  the  blowing  out  of  small  particles  of  broken  grain,  dust,  chaff,  etc. 
Likewise,  il  the  air  is  dry  there  is  usually  some  loss  of  water  in  the 
case  of  grain  of  comparatively  high  moisture  content.  On  the  other 
hand,  if  the  grain  is  cold  and  the  atmosphere  at  the  time  of  "running" 
is  warm  and  of  high  relative  humidity  there  may  be  sufficient  con- 
densation of  wat  ei'  iin  the  en  I  d  grain  to  cause  an  appreciable  increase 
in  weight.  Such  variations  as  these,  however,  depend  principally 
on  the  quality  and  condition  of  the  grain,  together  with  the  condition 
of  the  itmosphere  at  the  time  of  handling,  and  have  nothing  whatever 
to  do  with  the  difference  between  the  loss  in  weight  and  reduction  in 
moisture  content  as  treated  in  this  circular. 


I 


"  I *> u H <  t  in  9  •    Bureau  of  Plant  Industry,  1     S    Department 

3 


4  MOISTURE    CONTENT    AND    SHRINKAGE    IN    CHAIN. 

REDUCTION  OF  MOISTURE  AND   SHRINKAGE. 

Giving  due  consideration  to  the  loss  of  material  resulting  from  the 
handling  of  grain  through  an  elevator,  drier,  etc.,  the  reduction  in 
the  percentage  of  moisture  is  not  the  same  as  the  percentage  loss  in 
weight,  and  should  not  he  the  same  if  the  moisture  content  is  properly 
determined  and  the  weighing  done  correctly,  notwithstanding  the 
fact  that  water  is  the  only  substance  liberated  in  the  drying  process. 

WHY    THE    REDUCTION    OF   MOISTURE    AND   THE    SHRINKAGE    IN    GRAIN 
ARE    NOT    THE    SAME. 

The  difference  bet  ween  the  reduction  in  the  percentage  of  moisture 
and  the  shrinkage  exists  because  there  is  a  constant  change  of  base 
in  making  the  moisture  test.  Moisture  percentages  are  calculated  on 
the  basis  of  the  wet  sample,  i.  e.,  100  grams  of  grain  containing  20 
per  cent  of  moisture  consist  of  80  grams  of  dry  material  and  20  grams 
of  free  water.  For  the  purpose  of  demonstration  it  is  assumed  that 
this  100  grams  of  grain  containing  20  per  cent  of  moisture  be  dried 
until  the  weight  is  reduced  to  90  grams.  The  weight  has  therefore 
been  reduced  10  per  cent.  During  the  drying,  10  grams,  or  one-hajj 
of  the  water,  have  been  liberated  and  likewise  10  grams  still  remain  in 
the  grain,  but  the  remaining  10  grams  of  water  are  contained  in  the 
partially  dried  grain,  which  weighs  only  90  grams,  i.  e.,  ten-ninetieths, 
or  one-ninth  of  the  partially  dried  grain  is  water.  This  fraction 
expressed  in  percentage  is  equivalent  to  11.1  percent,  which  is  the 
moisture  content  of  the  remaining  90  grams  of  grain.  In  actual  prac- 
tice the  moisture  content  after  drying  would  not  be  determined  on  the 
90  grams  alone,  but  a  new  sample  of  100  grams,  the  same  weight  as 
was  used  for  the  original  test,  would  be  taken  and  this  would  contain 
11.1  grams,  equivalent  to  11.1  per  cent,  of  water. 

In  the  illustration  here  given  there  has  been  a  reduction  in  weight 
from  100  grams  to  90  grams,  or  a  shrinkage  of  10  per  cent.  The 
moisture  content  of  the  grain  has  been  lowered  from  20  per  cent 
before  drying  to  11.1  per  cent  alter  drying,  or  a  reduction  of  only  8.9 
per  cent.  The  shrinkage  in  weight  therefore  exceeds  the  reduction 
in  moisture  by  1.1  per  cent .  This  difference,  however,  is  not  constant 
but  depends  on  the  quantity  of  water  originally  contained  in  the 
grain  and  the  extent  to  which  the  drying  is  carried.  Moreover,  the 
difference  increases  irregularly  until  the  moisture  content  is  reduced 
approximately  one-half,  after  which  it  gradually  decreases  and  when 
I  he  free  w  ater  is  ent  irely  expelled  I  lie  difference  between  the  shrinkage" 
in  weight  and  the  reduction  in  moisture  content  equals  zero. 

These  variations  are  better  shown  in  Table  I.  in  which  the  original 
moisture  content  is  taken  as  25  per  cent.      Thefirst  part  of  the  table 

[Cir.  32] 


MOISTURE    CONTENl     \  M>    SHRINKAGE    IN    GRAIN. 


shows  the  reduction  in  moisture  contenl  resulting  with  each  I  percent 
of  shrinkage.  Thesecond  part  shows  the  shrinkage  corresponding  to 
each  1  percent  of  reduction  in  moisture. 

T  \m  i:   1 .     -  '"  "  the 

nal  moislur<  content  is  :■'<  per  cent. 


nkage  in  wei 

.lion 
iii 
mois 

shrin 

■  re- 
duction in 
moisture. 

in  moisture 
o   tent. 

Pa  ■ 

Shrii 
in  wei 

Fir  cent. 
1.31 

5  06 
7.41 

|  I  i 
10.71 
1 1 .  76 
12.79 
13.79 
14.78 
15.73 
16.67 
i;  58 
i-   18 

■ 

21.05 
21  87 

24  24 

25  00 

Exci 

shrin 
over  re- 
duction in 
a    ture. 

II 

.76 
1 .  53 

.!.  13 
;  12 

11.21 
12.21 

i  29 

-  ,  i 

21.15 

22    10 

- 
1.05 
1.21 

1 .  35 

1 .  58 
1.1.7 
1.73 
1.7s 
1.79 
1.79 
1.76 
1.71 
1   ill 
1   54 
1.41 
1 . 2.-1 
1.06 
.85 
.60 
.31 

oo 

Per  i 

0.00 

1 



.31 



■ 

1 







6 



1.41 

1.54 

- 

- 

1 .  64 

9 

1.71 

in 

1  76 

1 1 

1   79 

1.79 

- 

1 1 

1.73 

1.67 





- 

17 

17.  .. 

18 

18 

■ 

1.35 

1.21 





1.05 

21 

21 . . . 

-7 

- 

.17 

24 

24 

..'1 



.00 

HOW     THE      DIFFERENCE      BETWEEN      THE      REDUCTION      <  >l       MOISTURE 
\\l>    THE    SHRINKAGE    IN    GRAIN    CAN    BE    DETERMINED. 

While  these  differences  vary  with  the  original  moisture  content 
and  the  degree  of  drying,  they  can  be  determined  readilj  by  simple 
calculation. 

Shrinkage.  -To  find  the  final  weight  and  shrinkage  on  anj  given 
lot  of  grain  or  other  substance  which  has  been  dried,  the  original 
weighl  and  tin-  moisture  content  before  and  after  drying  being 
given,  the  following  simple  proportion  may  be  used: 

Pen  E  drj  mat-]  I'm     ata         'dry  mat-1    ..  /Originall     .    f   Final 

ter  after  drying        J         I       ter  before  drying       >  Weight. 

I'>\  multiplying  the  third  term  by  the  sen, ml  and  dividing  the 
product   l>\   the  first   term  the  quotienl  will  be  the  final  weight. 

Tin  i efi in   i in   original  h eight  !•  -    the  final  weighl  equal  brinl 

[f  tl riginal  weight   is  taken  as  100  per  cent,  which  can  always 

he  dune,  the  shrinkage  found  will  be  in  percentage,  but  if  it  is  desired 

[Clr.  .".•-•I 


()  .MOISTURE    CONTEXT    AND    SHRINKAGE    IN    GRAIN. 

to  express  the  shrinkage  in  terms  of  bushels  or  pounds  the    calcula- 
tion may  be  made  as  in   the   following  example: 

Problem. — What  will  be  the  shrinkage  in  weight  on  1,000  bushels  of  corn  if  the 
moisture  content  is  reduced  from  25  per  cent  to  \~>  per  cent? 

Dry  matter  after  drying  =  100  —  15  =  85  per  cent. 
Dry  matter  before  drying  =  100  —  25       75  per  cent. 
Original  weight  of  corn  =  1,000  bushels. 
Therefore  85  per  cent   :  75  per  cent  ::  1,000  bushels  :  final  weight. 

Completing  the  proportion  by  multiplying  1,000  by  7")  and  divid- 
ing the  product  by  85  the  final  weight  is  found  to  be  882.4  bushels, 
giving  a  shrinkage  equivalent  to  117.0  bushels,  or  11.76  per  cent. 
The  shrinkage  in  this  case  exceeds  the  reduction  in  moisture  content 
by  1.76  per  cent. 

For  additional  data  see  Tables  IT  and  TIL 

Moisture. — To  find  the  final  moisture  content  of  any  given  lot  of 
grain  or  other  substance  which  has  been  dried,  the  moisture  content 
before  drying  and  the  weight  before  and  after  drying  being  known, 
the  following  simple  proportion  may  be  used: 

Weight     1         /Original"!    ..    f  Percentage  of  dry  matter 

after  drying/         I  weight  /         I  in  original 

x  =  percentage  of  dry  matter  after  drying. 
Therefore  100  less  x  equals  the  percentage  of  moisture  remaining  after  drj  ing 

The  following  will  serve  as  an  example: 

Problem. — If  1,000  bushels  of  grain  containing  25  per  cenl  of  moisture  are  reduced 
to  900  bushels  on  drying,  what  will  be  the  percentage  of  moisture  in  the  dried  grain? 
900  bushels  :  1,000  bushels  ::  75  per  cent   :   t. 

Completing  the  proportion  by  multiplying  75  by  1,000  and  dividing 
the  product  by  900,  the  value  of  x  is  found  to  be  83.33  per  cent,  which 
is  the  percentage  of  dry  matter  remaining  after  drying.  Therefore 
100  per  cent  less  83.33  per  cent  equals  16.67  per  cent,  which  is  the 
moisture  content  of  the  dried  grain. 

The  grain  originally  contained  25  per  cent  of  moisture,  which  was 
reduced  to  16.67  per  cent,  or  a  decrease  in  moisture  content  of-8.33 
per  cent  as  the  result  of  drying.  At  the  same  time  the  weight  was 
reduced  from  1,000  bushels  to  900  bushels,  or  a  shrinkage  of  1(1  per 
cent.  The  shrinkage  in  weight,  therefore,  exceeded  the  reduction  in 
moisture  by  1.67  per  cent. 

For  additional  data  pertaining  to  moisture  see  Tables  ITT  and  IV. 

If  it  is  desired  to  find  the  original  moisture  content  when  the  final 
moisture  content  and  the  weight  before  and  after  drying  are  known, 
the  terms  of  the  foregoing  proportion  in  the  following  order  may  he 
used: 

Original"!    .    (Weight  after "I    ..    ("Percentage  of  drj  mat-"!  Percentage  of  dry  mat- 

weight  '        I      drying      J        I        ter  after  drying       J        1        ter  in  original. 

[Cir.  32] 


MOISTURE    CONTEND     \M>   SHRINKAGE    IN    GRAIN.  7 

Completing  the  proportion  in  the  same  manner  as  already  described 
and  subtracting  the  resull  so  obtained  from  100  per  cenl  will  give 
the  percentage  of  moisture  contained  in  the  grain  before  drying. 

EXPLANATION  OF  TABLES. 

Table  1 1  shows  the  loss  in  weight  resulting  from  the  partial  or  com- 
plete drying  of  grain  having  a  moisture  contenl  belov  II  per  cent. 
Thus,  if  the  original  moisture  content,  shown  at  the  top  of  each  col 
nmn  in  the  bodj  of  the  table,  and  the  reduction  in  moisture,  shown 
in  thf  column  on  the  left,  are  known  the  shrinkage  can  be  read  direct 
from  the  table.  For  example,  if  the  original  moisture  content  of  a 
sample  of  grain  is  19  per  cent  and  the  moisture  contenl  of  the  grain 
represented  by  such  sample  is  reduced  by  drying  to  15  per  cent, 
involving  a  1"--  of  moisture  of  \  per  cent,  proceed  as  follows:  Run 
down  the  coin  inn  under  the  heading  "  Loss  in  moisl  are,"  at  the  left  of 
the  table,  until  the  figure  I  is  reached  :  follow  the  line  of  figures  oppo- 
site I  to  the  right  as  far  as  the  column  headed  19  (original  moisture 
content  i.  The  4.70  percent  in  this  column  is  the  loss  in  weight,  or 
shrinkage,  which  corresponds  to  a  loss  of  1  per  cent  moisture  in  1!) 
per  cent  of  grain.  Had  the  original  moisture  content  been  26  per 
cent  the  loss  in  moisture  resulting  from  the1  drying  would  have  Keen 
II  per  cent.  In  column  26,  opposite  11,  is  12.94  per  cent,  which 
would  be  the  shrinkage  if  the  moisture  had  been  reduced  from  26  to 
1 5  per  cent  as  in  t  he  case  assumed. 

Table  III  differs  from  Table  II  in  that  it  shows  the  loss  in  moisture 
corresponding  to  each  unit  loss  in  weight.  The  method  of  reading 
the  table,  however,  is  t he  same. 

Table  [V  differs  from  Tables  11  and  Til  in  that  the  final  moisture 
content  can  be  read  direct.  This  table  will  he  of  special  value  to  op- 
erators of  grain  drier-  in  that  the  final  moisture  content  of  the  grain 
can  lie  ascertained  vm  closely  without  making  the  test,  provided 
the  moist  ure  eon i mi  of  the  grain  before  drying  and  the  weight  befi  re 
and  after  drying  are  known,  nol  of  course  taking  into  consideration 
an\  loss  due  to  t  lie  blowing  out  of  eh  all .  dirt,  etc.     The  readings  arc 

made  the  -a  me  a-  described  for  Table   II-   i.  e.,  in   t  he  coin  mil  <  in   t  he 

left  find  the  Dumber  corresponding  to  the  loss  in  weight;  opposite 
this  Dumber  in  the  column  indicating  the  original  moisture  content 
will  be  found  the  percentage  of  moisture  in  the  grain  after  drying. 
For  example,  if  the  original  moisture  content  is  20  per  cent  and  the 
loss  in  weight  is  5  per  cent  the  final  moisture  content,  as  shown  in 
column  20,  opposite  5,  is  found  to  be  15.79  per  cent. 

[Clr.32] 


8 


MOISTURE    CONTENT   AND    SHRINKAGE    IN    GRAIN. 


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[CIr.  32] 


M0IS1  I   1:1     CONTENI     \.\i»   SHRIN  K  LG1     I  \    GRAIN. 


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1 1 71  717171 


<-  71  '-   I-  . 

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—  —    — 1  —  — T,    ~,  r, 


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Tl       ^  — ■  *'  ri  —  .-'    (^o6oio-H    71  r^  —  .-"  . 


- 


*   ~ '  —   ~  '  "        -    '  -  -f.    -      -_      —  *  i   "7   —  ■  -        Z   \  -   f    T-   ~      — 


fCIr.  32] 


S  S2S3S2  SJ52SS  SSSJS  SS  SSSS 


10 


MOISTURE    CONTENT    AND    SHRINKAGE    IN    GRAIN. 


a 

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w 

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a 

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0 

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O 

o 

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a 
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HM©HO! 

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IQ  tCJ  CO  I^  00 

9.89 
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15.62 
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I  rii'.  32] 


MOISTUR]     CONTENT    IND  SHRINKAGE  IN    GRAIN. 


11 


-  T  *!  $  =   -      gSW  -  -     re  r.  t,  r-  o     IONNWC      3C  SIM —  .- 1     ,-  -  i  . 

.Ohhnw    wi»i  ■     '     -;  ct    —  ri  yi  ■-  CO    HN»«iij     c  so  ~-  _  n'     m  ■- 

--.  _,_____, n    mm:jm:i    :imm^>:    H^i*.-:- 


■  n  —  re  to    rj  r~.  a  — 


_3    Hr*fi^  59    neN«fli rou3    ~  re  r.  - 

•m     nr<r»nre     -..I--  —     -[---/ 

_^  —  ~~  — *  "'  "'  -    HNw^iuj    tet^odojg    —  ri  -e  —  -'    i -  y  -j  —  ri    -,•!.* 


sSSS 

ft"  =  —  —  ri  re    re  —  .-   -  c     i  -  /  ~-  z  -'    ■—  . 

_  _    ______    _  „ .-.,    ri  n  rt  r»  ri    ri  m  re  re  re    ::r:  ^ 


on   onvnc    nusvSh   oSconn  t-r*ooccc    —  re>:i~3 
ft"  G r  i  ri    —  —  ■-_:  t  -    i  -  x  ri  _'  «    NNn^uj    tc  r  -  x "  »  —    r  i  :e  — 

— '  — •    —  —  —<—.  — i    —  — .  —  —  n    :i  m  m  n  m    NMwmw    ce  re 


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,  _     _  _  „  r,  -,,     NM  c5  Oi  W     ?)  re  re  r-e 


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-^  „„„     _ 1 NNN 


r.  i  -  ■ :    —  - 1  —  c  c     as  o>  o>  co  S     ^  —   e  —  _r     x ^i !    .-:  = 

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reM—    ____^(     ^  — —  i,—     r, 


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_  _  _    _  _ _  _;i:iri:j  n  -i  n  f  i 


-     _ _.     —  ^c 

r  J  _ 

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™  —  — —    -  riririM    m  :i  m 


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r^  —  —  ri  re  re 


>  .-  ^  tJ  —  "^     »«!WN«    t-  ri 2b  CO  OCA  <o     —  >e  c  T-.  o 

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^  -  —  "•  ::  '■       -        -         '      *  _  —  _  rr    —.-'_•"  t- /     ~~  rire-e 


—  opi ' 


Cj«o    i-mc 


:-—"'■"—      *        .      •  ot      -~  —  rire—.ejr/r-     d  — «'     !     ! 
1    -.,  -.,  -., 


■ 

-  ■ '  -  -      _:  -  ■_■  i  -  i  -     /  *  -  r:  i :     i  ,  c 

C^  ~  —  "  -  :'--i~i    -i-iN/r'    ;'ri 


^  -  -  r  -'  —  r  i  -e    • 


[Clr.  32] 


-    r     —  ri  re  —  . 


i  -r  —  .  -     jr-.--r     -nr  -.:    CKsoac    —  f   ~  - 




12 


MOISTURE    CONTENT    AND    SHRINKAGE    IN    GRAIN. 


Ci  t—  co  r-  c 

»J  »-l  CO  «5  CO  I 


.  os  oo  r*  co  >o    m*  co  co  cm  --h    o  c  cc  ■-  o    f  ro  r  i  — 


r    X  t~  -o  >o  -r     co  CM  i-h  O  ©     00  t-  CO  "3  -f     co  CN  i-h 


^     I  -  'O  UZ  —  ro     01  — 


NHOOJQQ     t-  —  >--;  -r-  CO     N  r 


_•  CO  *-H  CO  ■*  CO 

.  —  :■:—'■:-: 

'  — '  ii7  ~v  ro  oi 


-v  h  _ : 


HO05  00N     CO  »C  -F  CO  CM     i-h 


p     "3  -f  CO  CM  •-<      O 


Q  COCO 

O  OS  00  t-  CO      "O  I-  CO  cm  M 


m«HO     OS  GO  I  -  CO  lO     -*  CO  CM  i— « 


►S  i— I  i— I  r-1  .— 1  i— I 


r     CO  CM  — i  O  O 


-HCO(NCn*t     NMCO 
»C  iO  iO  -r  f     CO  CM  t-H  O 

CO  t^  CO  iO  •*     CO  CM  r-1 


,J  CM  CM  -h  do  01 

CJ  >— I   CM  COCO  -* 

n'  c4 i-h  o oi oo, 


-  CO  >0>  M*  CO     CM  » 


r^OOOON     CO  «0  f  CO  CM     t-, 


ft,  Hi  2 


a,S 


OOXNO     •O-^cO^l'-H 


OS  CO  t-  rO  '  U3     T  CO  CM  >-H 


UOHHNN 

n  "  CO  t-^  O  iO  -* 


t^-  CO  »0  ■"*«  CO     CM  i-t 


CO  »C  f  CO  CM      i— i 


>0  **  CO  CM  -~t 


[Cir.  32] 


MOISTUR]     CONTENT    VND   SHRINKAGE    IN    GRAIN. 


L3 


r  r  —  ~  —     r  -  r.   r  t  ,  x     /  :i  r^  «  -     i x  x  —     -7  r  r  >-  —     r  i  —  t  -   -  .r  x  —  ~ 

■  -i  —    •  a  i  -  /  -  3    cr  3  c  c  _     r    ■  -  -  -  -    nnncc 

j    7.  —  —  eg  ri    ad  t  -  -z  •-  irf    — •  x  71  —  c :     /  --  x  — 


■ 
C  ?o  i  — •  —  i  - 

-    •  i - 1  -  ■•  t - 
K  x  ?:  >:  .-c  ^ 

•  r  -  X  x  -  i  — 
"*-  x  x  x  X  x 


71  N  71  71  71 


- 
—  X — 


■ 
71 71 


j  x  7i  —    o  *  i-  -  f    x  — 


r.  71  •*:  i-  : 


"  X  X  X  X  X 


> oo -* ©    ooosg    © « r^ -*■ oc 

» O     XI-U3MO     t*  «  »  K3  C 

--     -   -i  —  C       X   i-  >7  —  X 


■    -t  X  X 

t3  x  ^  —  X  _ 


if  ?"i  —  ■  -  t  - 


•xxxxx    xxx  we 


' 


-  •-  —    x  n  —  »  x    i-  •*:  -r  x - 


7:  x  _;  c  .  i  >  t 

_■  —  -.- 

**"  X  X  X  X  X 


- 1  r  -   f   t  -  X     C  -  ?l  '*  -      O^OO-hC 
t  -  —  * "  —  x     —  ~ i  i  ~  -r  —      SO  *c  OS  »0  C 


MN    ririn :  _  — : 


tj  X  --z  35  IM  • 


-t-  C  —  '-  '"■ 


I  71  71  71  71 


X  X   —  71  ~ 
—  —■■"■TO 

— '  —  3J  /  r  - 


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c-   /  i  -  -  o    x  m  —  —  —     X  -  <-  —  n    — 


x  —  x 


5  f-  c  —  x 


71  r4  m  7-  '  t 


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:  3  x    iq  i 


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—  -.--  -i 


—  —  -  f  -  - 


DM     -     ;  j_  r.  — 


—  x  n  -   — 


-  71  N  N  71  71      71  71  N  7t  71      71  - 


-- 

C  -  >  t  -    :' 


:  -r  x  ri  —    c  /  i  -  - 


•  t-  x  i-  O  — 

-     '  -    SfliTI" 
~-  71  71  71  71  71 


3    r  t  -  ■-  >*:     —  x-i—  ~      X  r-  J:  ■"  -r     71  — 


:  X     Plrtgaoc 


■  71  71  71  71  71     71  71  71  - 


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c-.  c:  _  —  —    — —  — .  j-t- 

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:  7i     — 


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71  ~  ■-     - 


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■  -^  Ifl  Ifl  M    - 


■ 


1  71  71  71  71 —  —  —      <—  —  —  —  — 


-  X  71  —   —       -    r   t  -  -Z   •"      X  71  — 


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-     --  C     ■     ■  *  i  —  ~  ~    /     1  -  -C.  -~  X :  71     — 


- 


>~  '"   —  X  71      — 


«3  -r  x  7i  — 


—     ■ —  —     • —  —  71  'iXXXX:: 


[Clr.32] 


UNIVERSITY  OF  FLORIDA 


3  1262  08928  9622 


